Quantification of Histochemical Staining by Color Deconvolution

Amout C. Ruifrok, Ph.D., and Dennis A. Johnston, Ph.D.

OBJECTIVE: To develop a flexible method of separation and quantification of immunohistochemical staining by means of color image analysis. STUDY DESIGN: An algorithm was developed to de­convolve the color information acquired with red-green­blue (RGB) cameras and to calculate the contribution of each of the applied stains based on stain-specific RGB ab­sorption. The algorithm was tested using different com­binations of diaminobenzidine, hematoxylin and eosin at different staining levels. RESULTS: Quantification of the different stains was not significantly influenced by the combination of multiple stains in a single sample. The color deconvolution algo­rithm resulted in comparable quantification independent of the stain combinations as long as the histochemical procedures did not influence the amount of stain in the sample due to bleaching because of stain solubility and saturation of staining was prevented. CONCLUSION: This image analysis algorithm pro­vides a robust and flexible method for objective immuno­histochemical analysis of samples stained with up to three different stains using a laboratory microscope, standard RGB camera setup and the public domain pro­gram NIH Image. (Analyt Quant Cytol Histol 2001; 23:291-299)

Keywords: image processing, computer-assisted; immunohistochemistry; color separation; color de­convolution.

Differential staining of cytoplasm, cell nuclei and other cell organelles, and specific proteins lies at the basis of pathology. One of the most common exam­ples is hematoxylin-eosin staining, with hema­toxylin (blue) staining mainly the cell nuclei and eosin (magenta-red) acting as a cytoplasmic stain. In addition to this, the ratio of hematoxylin and eosin staining of the cytoplasm indicates basophilia or acidophilia of the cytoplasm. Another common example of differential staining is the use of im.­munohistochemistry with, e.g., horseradish­peroxidase staining developed with 3,3' di­aminobenzidine (DAB) (brown). Immunohisto­chemistry techniques can result in highly specific staining of numerous antigens. Slides stained with multiple stains can be used for the cooccurrence and colocalization of different markers-for exam­ple, using a proliferation marker like Ki-67 together with a tumor-specific marker like the membrane­localized receptor Her2/Neu, diagnostic of specific breast tumors.

From the Departments of Pathology and Biomathematks, University of Texas M. D. Anderson Cancer Center, Houston, Texas, U.S.A.

Dr. Ruifrok is Assistant Professor, Department of Pathology.

Dr. Johnston is Professor, Department of Biomathematks.

Address reprint requests to: Arnout C. Ruifrok, Ph.D., Department of Pathology, Box 53, M. D. Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.

Financial Disclosure: The authors have no connection to any companies or products mentioned in this article.

Received for publication October 13, 2000.

Accepted for publication February 13, 2001.

0884-6812/01/2304-0291/$15.00/0 © The International Academy of Cytology Analytical and Quantitative Cytology and Histology 291

292 R111ti·ok and f o/111sfo11 • • • �d Quantitative Cytology and Histology· --

The goal of differential staining is to provide .in­dicators of the distribution of the substance or structures to which the stain specifically attaches. The amount of stain attached or deposited will then determine the optical density at stain-specific wave­lengths according, to the Lambert-Beer law,1 with optical density proportional to the stain concentra­tion. Although the dyes used for staining the differ­ent structures or proteins are visualized as having different colors, they actually mostly have complex overlapping absorption spectra. To simultaneously examine the photometric and morphometric fea­tures of one or more structures, the relative contri­butions of each of the dyes to the resulting absorp­tion spectrum, or the perceived colors, have to be separated. In regions with colocalization of the stains (e.g., staining with hematoxylin and DAB in Ki-67-positive nuclei), the quantification of each stain component cannot be determined at any sin­gle wavelength because the optical density at any such wavelength is determined by the total absorp­tion of the multiple stains.

To overcome the problem of separation of the contributions of multiple stains, three approaches have been used:

1. Use of individual components (stains) with nonoverlapping absorption bands. Although some successes have been reported using this ap­proach,2,3 unfortunately, current cytochemistry and histochemistry still offer only a very limited num­ber of such dyes.

2. Use of narrow-band filters to selectively mea­sure absorption at a dye-specific wavelength. Al­though a significant improvement in color separa­tion has been made using this technique, it still suffers from partial overlap in the absorption spec­tra of different dyes.4-7 Matched filters are needed for every stain used; that may require considerable expense. Even with specifically matched filters, it is difficult to design a system so that each stain ap­pears completely separated into a single color chan­nel. Narrow-band filtering changes the color repre­sentation and reduces the color saturation in displays.

3. Use of color transformation techniques based on red-green-blue (RGB) broad-band information from analog or digital three-channel cameras. Con­siderable success has been shown using color transformation techniques, using either the hue­saturation-intensity (HSI) transformation6,7 or sim- . ilar transformations, such as hue-value-chromas or stain-specific transformation.9,.10 A disadvantage of

color transformation techniques is that although the existing color transformations do result in segmen­tation based on color, they do not result in the sep­aration of the contributions of two or more stains to the resulting color. Areas that are stained with two or more dyes are designated one of the colors, de­pending on the relative contributions of the stains and threshold settings. This can result in consider­able information loss when the above transforma­tion techniques are used.

In histologic and cytologic staining it is hardly ever the case that areas are stained for one color only. This means that considerable information is lost when the above transformation techniques are used. Therefore, we developed a novel color­deconvolution method that makes use of the broad­band RGB information of standard analog or digital three-channel cameras. The method can be used for separation of practically every combination of two or three colors, provided that the colors are suffi­ciently different in their red, green or blue absorp­tion characteristics. As the RGB sensitivity of cameras is matched to the RGB sensitivity of the human visual system, virtually every set of three colors that can be seen as different colors by eye also can be separated by the color-deconvolution method. The method is based on orthonormal transformation of the original RGB image, depend­ing on user-determined color information about the three colors. The method provides the possibility to determine staining densities, even in areas where multiple stains are colocalized, making it possible not only to determine surface area and overall ab­sorbtion in areas with a specific color but also to de­termine densities and ratios of densities of stains in each area. After color deconvolution, images can be reconstructed for each stain separately and be used for densitometry and texture analysis for each stain, using standard imaging methods. _

#

Theory Color Representation In this discussion we assume a video microscopy system with an RGB camera, assuming that gray levels in each of the RGB channels are linear with brightness or transmission T, with T being I/10, with Io being the incident light and I the transmitted light. This assumption is reasonably accurate for CCD cameras with a gamma of 1.0.

Each pure stain will be characterized by a specif­ic absorption factor, c, for the light in each of the three RGB channels. The detected intensities of light

Volume 23! Number 4/August 2001 · :f ;.,::-·· . ·

· Quantification of H1stochemical St1ining 293

transmitted through a specimen and the amount (A) of stain with the absorption factor, c, are de­scribed by Lambert-Beer's law,1

le Io,c exp(-Acc),

with Io,c the intensity of light entering the speci­men, Ic the intensity of light detected after passing the specimen and subscript c indicating the detec­tion channel. This means that the transmission of light, and therefore the gray values of each charmel, depend on concentration of stain in a nonlinear way.

In the RGB model, the intensities IR, le and IB are obtained by the camera for each pixel. Because the relative intensity in each of the channels depends on the concentration of stain in a nonlinear way,11 the intensity values of the image cannot directly be used for separation and measurement of each of the stains. However, the optical density (00) for each channel can be defined as

ODc =-log10(1c/lo,d =A ,.cc

The OD for each channel is linear with the con­cent:Tation of absorbing material and can therefore be used for separation of the contributions of multi­ple stains in a specimen.

Each pure stain will be characterized by a specif­ic OD for the light in each of the three RGB chan­nels, which can be represented by a 3x1 OD vector describing the stain in the OD-converted RGB color space. For example, measurements of a sample stained with only hematoxylin resulted in OD val­ues of 0 . 18, 0.20 and 0.08 for the R, G and B chan­nels, respectively.

The length of the vector will be proportional to the amount of stain, while the relative values of the vector describe the actual OD for the detection channels. In the case of three channels, the color sys­tem can be described as a matrix of the form

[ pll p12 p21 p22 p31 p32

p13] p23 p33

With every row representing a specific stain and every column representing the OD as detected by the red, green and blue channel for each stain. Stain-specific values for the OD in each of the three channels can be easily determined by measuring relative absorbtion for red, green and blue on slides stained with a single stain. An example of the OD matrix for the combination of hematoxylin, eosin and DAB is:

R [ 0.18

0.01 0.10

G 0.20 0.13 0.21

B 0.08] 0.01 0.29

Color Deconvolution

Hematoxylin Eosin DAB.

To perform separation of the stains, we have to do an orthonormal transformation of the RGB infor­mation to obtain independent information about each stain's contribution. The transformation has to be orthogonal to achieve independent information about each of the stains; the transformation has to be normalized to achieve correct balancing of the absorbtion factor for each separate stain.

For normalization, we divide each OD vector by its total length,

Pn =p11!'1Pr1 +Pf2+P13'

P21 =P21!'1P?1 +ph+pb,

P31 =p31/;/P�1 +p�2+p&,a and so forth, resulting in a normalized OD matrix, M:

p21 p22 p23 [pl l p12 p13]

p31 p32 p33 .

The normalized OD matrix, M, for the above com­bination of hematoxylin1 eosin and DAB is:

0.07 0.99 0.11 [ 0.65 0.70 0.29 l

0.27 0.57 0.78 .

If C is the 3 x 1 vector for amounts of the three stains at a particular pixel, then the vector of OD levels de­tected at that pixel is y =CM.

From the above it is clear that C=M·l(y]. This means that multiplication of the OD image with the inverse of the OD matrix, which we define as the color-deconvolution matrix, D, results in orthogo­nal representation of the stains fonn:iilg the image:

C=D [y].

D, corresponding to M for the hematoxylin, eosin and DAB matrix, is:

[ 1.88 1.02

-0.55

-0.07 1.13

-0.13

-0.60] -0.48

1.57 '

In this matrix, the diagonal elements are greater than unity,_ whil�J:h� off:di!lgonal elements ar�_neg-_

294 /�1nfro/, 011d folmston . · al'�d Quantitative Cytology and Histology

-�·

ative. The above equation implies that the corrected OD level values for each stain are formed by sub­tracting a portion of the green OD and blue OD from the enhanced red OD to obtain the hema­toxylin OD, subtracting a portion of the red OD and blue OD from the enhanced green OD to obtain the eosin OD and subtracting a portion of the red OD and green OD from the enhanced blue OD to obtain the DAB OD. In case the stains used would be pUie red, green and blue, the above matrix would be the unity matrix.

Results of experiments using the above method are presented below. Combinations of different staining intensities on the same slides were per­formed to test the influence of different levels of eosin counterstair\ on the quantification of DAB and hematoxylin.

Materials and Methods Specimens

Sectons from a breast tumor specimen were stained for Her2/neu expression with Her2/neu-specific antibody (Oncogene Science, Cambridge, Massa­chusetts, U.S.A.) and DAB chromogen (Biogenics, Napa, California, U.S.A.). Counterstaining was per­formed with Mayer's Hematoxylin (Richard Allan, Kalamazoo, Michigan, U.S.A.) for three to five min­utes and eosin (Polyscientific, Bay Shore, New York, U.S.A.) for different periods under visual con­trol. Sections from a lung tissue specimen were stained with Mayer's Hematoxylin (Richard Allan) for three to five minutes and eosin (Polyscientific) for different periods under visual control. For de­termination of the effect of different eosin-staining levels on DAB and hematoxylin staining measure­ments, slides were destained in 95% alcohol or demineralized water and restained with eosin for different periods to reach a range of eosin staining intensities. Corresponding areas of slides were ana­lyzed after each staining step, and stained area, OD and integrated OD (IOD) were determined.

Image Acquisition

A Leica DMLB microscope (Leica Microsystems Inc., Deerfield, Illinois, U.S.A.) was equipped with a Hamamatsu C5810 chilled three-chip color CCD camera (Hamamatsu, Bridgewater, New Jersey, U.S.A.) interfaced with an IBM computer (Interna­tional Business Machines Corporation, Armonk, New York, U.S.A.) equipped with a Matrox Meteor digitizer board (Matrox Electronic Systems Ltd., Dorval, Queb�, Canada).

Light and camera settings were standardized, re­sulting in average background values of 20±5 (mean ±SD, scale 0-255 from white to black) for the red, green and blue channels. Linearity of the image-acquisition setup was tested using a stepped neutral density filter and was found to be linear with light intensity for all three colors within 2% over the whole dynamic range of the camera (corre­lation coefficients of the OD with grayscale values for red, green and blue: R > .996, R2 > .993). The im­ages were captured with 20x (lung tissue) and 40x (breast tissue) objective lenses.

Image Processing

The 24-bit RGB images were transferred to a Macin­tosh G4 computer (Apple Computer, Cupertino, California, U.S.A.) and processed and analyzed using NIB image version 1.62, developed at the Na­tional Institutes of Health and available on the in­ternet from http://rsb.info.nih.gov/nih-image/. Custom macros were written for background cor­rection and transformation from intensity to OD to determine the color vectors for the different stains, for calculation of the color-deconvolution matrix and for the actual color deconvolution of the im­ages. The stored image of an empty field was used for determination of the light entering at each pixel (10), implicitly correcting for unequal illumination background subtraction.

Test of the System Performance

To test the performance of the deconvolution algo­rithm, different staining combinations were quanti­fied on the same areas of tissue sample. Quantifica­tion of DAB staining was performed by repeated measurement of samples stained with only DAB, DAB plus hematoxylin and DAB plus hematoxylin plus eosin at different levels. To test the influence 0£ eosin staining on the quantification of hematoxylin, repeated measurements were performed with sev- . eral levels of eosin staining. The interaction of the stains with respect to quantification of each sepa­rated stain was compared using the analysis of co­variance. lbis was accomplished using SPSS (SPSS, Inc., Chicago, Illinois, U.S.A.) and the custom pro­gram AOC (www.odin.mdacc.tmc.edu). This pro­cedure follows the general plan described by Zar.12 Descriptive comparison of performance was done using the measures mean shift, scale factor (ratio of the SDs), precision (equal to the correlation coeffi­cient), accuracy (mixture of the means and SDs) and con�orda!lse _(prg�L!ct of precisio!.l_and. �scur�cy_1 a..!>

Volume 23, Number 4/August 2001 :��11;. _. Quantification of Histochern1ral Sl;i1nmg 295

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Figure 1 (A) Photomicrograph of a breast tissue slide stained with DAB {brown), hematoxylin (blue) and eosin (magenta). (B-D) Color-deconvolution results separating the contributions of hematoxylin (8), eosin (C) and DAB (D) to the original image (x40, bar=20 µm).

described by Fisher and van Belle.13 With optimal reproducibility, the mean shift centers around 0, the scale factor centers around l, and precision, accura­cy and concordance maximize to 1.

Results

Figure 1 shows a representative example of DAB, hematoxylin and eosin staining before and after color deconvolution. The result is a set of three im­ages showing continuous representation of· the three contributing stains.

To test the performance of the color­__ deconv.olution algorithm under different circ�-

stances, we compared quantification of the stains using different combinations and concentrations. Descriptive comparison of performance was done using the measures mean shift, scale factor, preci­sion, accuracy and concordance, as described by Fisher and van Belle.13 With optimal reproducibili­ty, the mean shift centers around 0, the scale factor centers around 1, and precision, accuracy and con­cordance maximize to 1.

Addition of hematoxylin staining to the slides did not result in significant changes in the mea­sured IOD of DAB staining (Figure 2). The mean shift of the IOD measurements was <-0.05, and-the ...

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scale factor was > 0.95. With a precision of > 0.99, this resulted in an accuracy of > 0.99 and concor­dance of >0.99.

When hematoxylin and eosin both were added to the DAB-stained slides, no difference in slope was observed (P = .281 ), but a significant mean shift (P < .001) was seen (Figure 2). This indicates a dif­ference in level but no interaction of stains that would change the rate of DAB quantification. Al­though after addition of eosin a significant mean shili to higher IOD values was observed, the scale factor was 0.95. Because of the high precision (0.99) and the high accuracy (0.98), the resulting concor­dance (0.97) still was high.

To further study the influence of eosin staining on the DAB quantification, we measured the DAB IOD with different levels of eosin counterstain. Eosin staining was added, or "bleached," by incu­bating the slides in 95% alcohol or distilled water until an appreciable reduction in eosin staining was observed. This way, eosin concentration was in­creased and reduced to about 75% and 40% of the initial concentration. There were no signlficant dif­ferences in slope (P = .738) or mean (P .193) of DAB quantifications, indicating that the three eosin levels did not significantly inferfere-...with.. DAB

quantification (Figure 3). Even after these multiple rounds of processing, the DAB measurements showed precision, a<;curacy and concordance of> 0.99, with mean shifts of <0.1 and scale factors of 0.98-1.00. These data clearly show the stability of the stain and robustness of the quantification proce­dure.

Finally, to study the interaction between hema­toxylin and eosin quantification, we stained and destained sections of lung tissue stained with hematoxylin and different levels of eosin. The re­sults of these experiments are shown in Figure 4. Quantification of hematoxylin decreased after ma­nipulation of eosin staining. The first eosin staining resulted mainly in a mean shift of the measure­ments to lower values, with a mean shift value of 0.59, while the scale factor was 1.06. With precision of> 0.99, this resulted in accuracy and concordance of 0.84.

To determine whether this was the result of inter­ference of the colors in the quantification process or came from actual reduction of the staining due to technical artifacts (bleaching of hematoxylin during eosin staining), we repeatedly destained and

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Figure 3 Influence of different levels of eosin staining on the quantification of DAB and eosin in breast tissue sections. The IOD measurement for DAB and eosin in areas stained with different amounts of eosin was plotted against the IOD measurements for DAB and eosin staining (first staining) alone in the same areas. In the first eosin staining step, eosin was added (100%); in the following two steps increasing amounts of eosin were bleachecf_from the .slide (to about 75% and 40%}.

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Volume 23, .Number 4/ August 2001 8� ·1} ., ; ,'" Quantification of H1stochem1cill Stilm111� 297

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figure 4 Influence of different levels of eosin staining on quantification of hematoxylin in lung tissue sections. The IOD measurement for hematoxylin and eosln in areas stained with different amounts of eosin was plotted against the !OD measurements for DAB and eosin sta in ing (first staining) alone in the same areas. In the first eosin staining step eosin was added (100%), in the second and third steps increasing amounts of eosin were bleached from the slide (to about 71% and 27%), and in the fourth step eosin was added again (to about 51 %).

restained the samples with eosin. The slopes were significantly different (P = .0096), with the change showing a dose/response relationship with the re­peated treatments (adding or bleaching) of eosin, reducing the slope (0.943 to 0.792, respectively) ver­sus hematoxylin alone. This happened regardless of whether the eosin staining increased or decreased. Therefore, we conclude that the decrease in hema­toxylin measurements was the result of reduction of the amount of stain during processing, due to bleaching in aqueous media, not due to interference of quantification of the two stains ..

Discussion

Image analysis for the quantification of differential cytochemical or immunohistochemical staining has the advantage over biochemical assays and flow cy­tometry that it is nondestructive and that informa­tion concerning the relation between morphology and the cell organelle or protein under study is maintained. In addition, automated analysis is fast�r, _more obj�ctive and less laboriogs_ lhan visual

examination. Segmentation and density mea5ure­ments can be performed using interactive as well as computer-determined thresholds. However, over­lap in spectral absorption by the stains used can be a major problem.

Several methods have been proposed in attempts to obtain independent information about the stain concentrations in histologic and cytologic speci­mens. Some of the systems try to limit either the spectral overlap of the stains (monochromatic dyes) or the spectral overlap of the detection system (nar­row band filters). The use of monochromatic dyes was limited by the availability of such dyes. The use of a narrow-band filter sometimes requires expen­sive filters and results in a reduced signal, which may compromise the signal-to-noise ratio of the image and thereby reduce the reliability of the measurements. Even with the use of narrow-band filters, overlap in absorption in the specific wave­length regions may occur, resulting in incomplete elimination of the respective chromogens.7

Another category of methods uses basic RGB in­formation or a transformation of this information into, e.g., HSI or color-specific components for seg­mentation of the image in areas of different colors. These color separation techniques use one of the transformed values (e.g., hue or chroma) for color classification by some thresholding technique. The classification of pixels is exclusive; each pixel is des­ignated as one of the targeted colors or hues. How­ever, as absorbtion of different colors contributes to the overall red, green and blue absorption and as such also to the overall hue, saturation and intensi­ty, color separation can no longer be achieved reli­ably.

We present a color deconvolution algorithm that uses the information on all contributing colors. It can be used on standard RGB images, as acquired with a standard, three-channel analog or digital camera. Processing can be performed quickly and easily on a Macintosh computer using custom macros written for the public domain program NIH image. This means that for the price of a good three­chip CCD camera and digitizer board, it is possible to perform quantitative histochemical analysis.

The present method of color deconvolution al­lows the separate presentation of stain components even if the stains show overlapping spectral ab­sorption spectra as well as colocalization. Measure­ment of the color vectors of the specific stains can easily be determined on single-stained specimens.

__ ,.In case of-interaction between st.a.ins, the user·can-

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Figure 5 {A) Photomicrograph of a breast tissue slide stained with saturating levels of DAB {brown). (B-D) Color-deconvolution results showing the apparent contribution of hematoxyl in {B) and eosin (C) (x 40, bar= 20 µml.

select areas of the multiple-stained slides as repre­sentative of the color to be measured. The method overcomes the disadvantages of filtering tech­niques or RGB or HSI color segmentation tech­niques. The color deconvolution technique allows insight into the biochemical composition of a tissue because it leads to accurate quantification of the rel­ative distribution of each stain.

As shown above, addition of hematoxylin or eosin to DAB staining hardly influences DAB quan­tification. Eosin staining also does not seem to in­fluence hematoxylin quantification, apart from the histotechnical complication of bleaching the stain.

Because hematoxylin and eosin are soluble in aqueous media, it was not possible to reliably de­..termine the influence of the addition-of DAB. to- -

eosin or hematoxylin quantification. However, we did apply the above algorithm to DAB­only-stained sections to make an estimate of the possible (erroneous) contribution of DAB staining to hematoxylin and eosin quantification. Erroneous deconvolution may especially be· the result of satu­ration of staining and signal detection. As it is clear that saturation of a signal makes it impossible to perform accurate quantification, all color separa­tion techniques, including the present one, will re­sult in erroneous measurements when saturation takes place. Therefore, extremely dark DAB stain­ing may result in an erroneous measurement of a "hematoxylin" signal and "eosin" signal even if these colors are not actually present. Wf!! had ex­tremely dark DAB stammg.in some areas of the

ir. • .- • ·. _. . Quantific,1tion of Hi�toche::m1cnl St;.iining 299 Volume 23, Number 41August 2001 · ·1�1

slides; an example is given in Figure 5. As can be clearly seen, the very dark areas of the DAB-stained slide also contributed to the hematoxylin and eosin image. As a result of this, the possible contribution of DAB-saturated areas to the measured IOD for hematoxylin reached an average of 65%. Eosin quantification was less influenced by this phenom­enon: only about 8% of the IOD measured at the lowest eosin staining level could possibly have con­tributed to saturation of DAB staining, while the mean amount was only 3% for the darkest eosin staining.

The present data show that chromogen quantifi­cation is not significantly influenced by addition of a second or third color but mainly by the stability of the chromogens used in the staining procedure as long as saturation of staining in each of the colors is prevented. This means that using the presented color separation technique, the reliability of the measurements depends mainly on the quality of the sample input, stressing the importance of the use of standard methods, inclusion of standard samples and prevention of signal saturation.

Acknowledgments

The authors thank Sejal Patel and Abha Khana for their expert technical assistance.

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